viscosity_kernel.f90

!Crown Copyright 2012 AWE.
!
! This file is part of CloverLeaf.
!
! CloverLeaf is free software: you can redistribute it and/or modify it under 
! the terms of the GNU General Public License as published by the 
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! any later version.
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!>  @brief Fortran viscosity kernel.
!>  @author Wayne Gaudin
!>  @details Calculates an artificial viscosity using the Wilkin's method to
!>  smooth out shock front and prevent oscillations around discontinuities.
!>  Only cells in compression will have a non-zero value.

MODULE viscosity_kernel_module

CONTAINS

SUBROUTINE viscosity_kernel(x_min,x_max,y_min,y_max,    &
                            celldx,celldy,              &
                            density0,                   &
                            pressure,                   &
                            viscosity,                  &
                            xvel0,                      &
                            yvel0                       )

  IMPLICIT NONE

  INTEGER     :: x_min,x_max,y_min,y_max
  REAL(KIND=8), DIMENSION(x_min-2:x_max+2)                     :: celldx
  REAL(KIND=8), DIMENSION(y_min-2:y_max+2)                     :: celldy
  REAL(KIND=8), DIMENSION(x_min-2:x_max+2,y_min-2:y_max+2)     :: density0
  REAL(KIND=8), DIMENSION(x_min-2:x_max+2,y_min-2:y_max+2)     :: pressure
  REAL(KIND=8), DIMENSION(x_min-2:x_max+2,y_min-2:y_max+2)     :: viscosity
  REAL(KIND=8), DIMENSION(x_min-2:x_max+3,y_min-2:y_max+3)     :: xvel0,yvel0

  INTEGER       :: j,k
  REAL(KIND=8)  :: ugrad,vgrad,grad2,pgradx,pgrady,pgradx2,pgrady2,grad     &
                  ,ygrad,pgrad,xgrad,div,strain2,limiter

!$OMP PARALLEL

!$OMP DO PRIVATE(ugrad,vgrad,div,strain2,pgradx,pgrady,pgradx2,pgrady2,limiter,pgrad,xgrad,ygrad,grad,grad2)
  DO k=y_min,y_max
    DO j=x_min,x_max
      ugrad=(xvel0(j+1,k  )+xvel0(j+1,k+1))-(xvel0(j  ,k  )+xvel0(j  ,k+1))

      vgrad=(yvel0(j  ,k+1)+yvel0(j+1,k+1))-(yvel0(j  ,k  )+yvel0(j+1,k  ))

      div = (celldx(j)*(ugrad)+  celldy(k)*(vgrad))

      strain2 = 0.5_8*(xvel0(j,  k+1) + xvel0(j+1,k+1)-xvel0(j  ,k  )-xvel0(j+1,k  ))/celldy(k) &
              + 0.5_8*(yvel0(j+1,k  ) + yvel0(j+1,k+1)-yvel0(j  ,k  )-yvel0(j  ,k+1))/celldx(j)

      pgradx=(pressure(j+1,k)-pressure(j-1,k))/(celldx(j)+celldx(j+1))
      pgrady=(pressure(j,k+1)-pressure(j,k-1))/(celldy(k)+celldy(k+1))

      pgradx2 = pgradx*pgradx
      pgrady2 = pgrady*pgrady

      limiter = ((0.5_8*(ugrad)/celldx(j))*pgradx2+(0.5_8*(vgrad)/celldy(k))*pgrady2+strain2*pgradx*pgrady)  &
              /MAX(pgradx2+pgrady2,1.0e-16_8)

      IF ((limiter.GT.0.0).OR.(div.GE.0.0))THEN
        viscosity(j,k) = 0.0
      ELSE
        pgradx = SIGN(MAX(1.0e-16_8,ABS(pgradx)),pgradx)
        pgrady = SIGN(MAX(1.0e-16_8,ABS(pgrady)),pgrady)
        pgrad = SQRT(pgradx*pgradx+pgrady*pgrady)
        xgrad = ABS(celldx(j)*pgrad/pgradx)
        ygrad = ABS(celldy(k)*pgrad/pgrady)
        grad  = MIN(xgrad,ygrad)
        grad2 = grad*grad

        viscosity(j,k)=2.0_8*density0(j,k)*grad2*limiter*limiter
      ENDIF

    ENDDO
  ENDDO
!$OMP END DO

!$OMP END PARALLEL

END SUBROUTINE viscosity_kernel

END MODULE viscosity_kernel_module